Details

Time bar (total: 38.3s)

sample142.0ms

Algorithm
intervals
Results
48.0ms254×body160nan
44.0ms550×body80nan
25.0ms256×body80valid

simplify21.6s

Counts
1 → 1
Iterations
IterNodes
94745
81502
7489
6252
5117
466
335
219
115
07

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (fma x x -1))))
0.0b
(+ x (sqrt (fma x x -1)))
34.3b
(sqrt (fma x x -1))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 52
Calls
3 calls:
7.0ms
(log (+ x (sqrt (fma x x -1))))
7.0ms
(+ x (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))

series314.0ms

Counts
3 → 9
Calls
3 calls:
152.0ms
(log (+ x (sqrt (fma x x -1))))
76.0ms
(+ x (sqrt (fma x x -1)))
86.0ms
(sqrt (fma x x -1))

simplify4.0s

Counts
61 → 61
Iterations
IterNodes
46802
31976
2680
1267
0119

prune575.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))
0.1b
(* x (* x x))
0.2b
(/ -1/8 (* x (* x x)))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt
43×*-un-lft-identity
41×add-cube-cbrt
39×prod-diff
31×times-frac
17×pow1 add-cbrt-cube add-exp-log
6×prod-exp cbrt-unprod
5×pow-prod-up add-log-exp
4×div-inv
3×expm1-log1p-u cbrt-undiv fma-neg div-exp associate-*l* pow-prod-down insert-posit16 log1p-expm1-u associate-/l*
2×difference-of-squares
1×pow2 clear-num associate-/r* sub-neg frac-2neg pow-plus flip3-- diff-log cube-unmult associate-*r* associate--l+ pow-sqr *-commutative fma-udef flip-- distribute-lft-out-- unswap-sqr
Counts
3 → 114
Calls
3 calls:
15.0ms
(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))
29.0ms
(* x (* x x))
27.0ms
(/ -1/8 (* x (* x x)))

series214.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(- (fma x 2 (/ -1/8 (* x (* x x)))) (/ 1/2 x))
64.0ms
(* x (* x x))
82.0ms
(/ -1/8 (* x (* x x)))

simplify2.2s

Counts
123 → 123
Iterations
IterNodes
34988
21465
1534
0231

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (log (+ x (sqrt (fma x x -1)))))
34.3b
(sqrt (fma x x -1))
34.3b
(sqrt (fma x x -1))
34.3b
(sqrt (fma x x -1))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×pow1 *-un-lft-identity add-cube-cbrt
4×cbrt-prod expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3 log-pow
Counts
4 → 63
Calls
4 calls:
1.0ms
(cbrt (log (+ x (sqrt (fma x x -1)))))
1.0ms
(sqrt (fma x x -1))
1.0ms
(sqrt (fma x x -1))
1.0ms
(sqrt (fma x x -1))

series581.0ms

Counts
4 → 12
Calls
4 calls:
342.0ms
(cbrt (log (+ x (sqrt (fma x x -1)))))
82.0ms
(sqrt (fma x x -1))
78.0ms
(sqrt (fma x x -1))
78.0ms
(sqrt (fma x x -1))

simplify1.9s

Counts
75 → 75
Iterations
IterNodes
33150
2818
1291
0123

prune930.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
212
112
011

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.4s7648×body160nan
1.3s16362×body80nan
1.1s8000×body80valid